PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
6001(28*10^85500+149)/385501Robert Price10/2017
6002(16*10^85495-19)/385496Robert Price03/2016
60032^284004+17785494Lelio R Paula08/2012
6004(16*10^85473-91)/385474Robert Price06/2016
60053^179120+2285462Robert Price12/2013
60062^283872-279224985454Enzo Doria03/2016
6007(29*10^85438+259)/985439Robert Price04/2017
60082^283817+8287585438Lelio R Paula09/2013
6009(2^283815-5)/20185435Lelio R Paula01/2013
60102^283796-12585432Lelio R Paula08/2012
6011(29*2^283784-1)/1385428Lelio R Paula02/2014
601215^72592-2885375Lelio R Paula11/2015
60132^283604-5869585374Lelio R Paula09/2013
6015(44*10^85370-503)/985371Robert Price10/2017
6014(2^283597+1854)/285371Stefano Morozzi01/2020
6016496^31671+31671^49685369Norbert Schneider07/2017
6017(2^283578+478)/285366Stefano Morozzi01/2020
6018(15*2^283583-1)/10305185364Lelio R Paula02/2014
601915^72572+9285352Lelio R Paula11/2015
60202^283473-161585334Lelio R Paula09/2013
6021(2^283469+2934)/285333Stefano Morozzi01/2020
60222^283466-1585332Lelio R Paula08/2012
6023(2^283437+3446)/285323Stefano Morozzi01/2020
6024(2^283411+3894)/285315Stefano Morozzi01/2020
602511^81916-702085307Enzo Doria02/2013
60266^109626-785306Lelio R Paula11/2014
60272^283374-11032785305Enzo Doria05/2014
602833*10^85297+785299Robert Price07/2016
602918^67933+4185275Lelio R Paula11/2015
60302^283271-10934185274Enzo Doria04/2014
6031(2^283266+3678)/285272Stefano Morozzi01/2020
603219688^19855-19855^1968885262Norbert Schneider03/2020
6033(2^283216+1926)/285257Stefano Morozzi01/2020
6034(25*10^85249-73)/385250Robert Price09/2016
60352*5^121959+385246Lelio R Paula10/2014
603619834^19834+894785235Henri Lifchitz11/2004
60372^283140+191585234Lelio R Paula09/2013
60383*10^85227-9785228Robert Price08/2017
6039(16*10^85221-31)/385222Robert Price03/2016
6040(2^283096+3186)/285221Stefano Morozzi01/2020
60412^283083+186938385217Enzo Doria05/2016
6042(24737*2^283051+1)/1785211Lelio R Paula06/2014
6043(2^283032+78557)/385201Lelio R Paula01/2013
60442^283026-10989385200Enzo Doria04/2014
6045(2^283012+78557)/12985193Lelio R Paula01/2013
6046(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
60472^282860-10972785150Enzo Doria04/2014
6048(2^282847+13)/385145Stefano Morozzi03/2020
60492^282819+186941385138Enzo Doria05/2016
60503^178428+285132Ray Chandler07/2011
6051(22699*2^282742+1)/7385117Lelio R Paula06/2014
6052(16^70687+5^70687)/2185115Robert Price07/2013
6053(2^282732+738)/285111Stefano Morozzi01/2020
6054(2^282720+1590)/285107Stefano Morozzi01/2020
6055(3^178352-2)/785095Lelio R Paula12/2012
605611^81699-279085081Enzo Doria12/2012
60572^282612-9585075Lelio R Paula08/2012
60582^282609-406985074Yves Minet02/2018
605975^45366-285065Lelio R Paula08/2013
6060(2^282550+1918)/285056Stefano Morozzi01/2020
6061(2^282515+3786)/285046Stefano Morozzi01/2020
60622^282511+6985045Lelio R Paula08/2012
606369^46249+285045Lelio R Paula06/2013
6064(2^282488+2382)/285038Stefano Morozzi01/2020
6065(2^282489+1862)/285038Stefano Morozzi01/2020
60663^178226+1085036Robert Price10/2013
6067(2^282475+1050)/285034Stefano Morozzi01/2020
6068(182*10^85017+43)/985019Robert Price11/2017
6069(14*10^85010+73)/385011Robert Price04/2016
60709*2^282338-784994Lelio R Paula08/2014
6071(9913*2^282330-1)/157800384988Lelio R Paula04/2015
60722^282203+584952Lelio R Paula08/2012
60732^282184+1384946Lelio R Paula08/2012
607411^81568-240084945Enzo Doria12/2012
607511^81562-234084939Enzo Doria12/2012
6076(41*10^84927+31)/984928Robert Price05/2015
6077(2^282053+1406)/284907Stefano Morozzi01/2020
6078(2*10^84904-17)/384904Robert Price08/2014
6079(4^141017+23)/384901Robert Price02/2017
60806^109100-1865384897Enzo Doria03/2013
60812^281973+102584883Lelio R Paula09/2013
60822^281951-10965184876Enzo Doria04/2014
608311^81491-543084865Enzo Doria01/2013
6084((1+sqrt(3)+sqrt(2))^79357-1)*((1+sqrt(3)-sqrt(2))^79357-1)*((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(384849Mike Oakes04/2009
6085(2^281827+650)/284839Stefano Morozzi01/2020
60862^281825-186148384838Enzo Doria03/2016
60872^281809-9730584833Lelio R Paula09/2013
60882^281780-11489384825Enzo Doria05/2015
60893^177719+6484794Lelio R Paula12/2015
60912^281675-19984793Lelio R Paula08/2012
60902^281673-11122384793Enzo Doria05/2014
6092(4*10^84779+149)/984779Robert Price03/2017
6093129^40167-12884777Norbert Schneider01/2019
6094(2^281622+3970)/284777Stefano Morozzi01/2020
6095(72*10^84772-27)/984773Ray Chandler01/2011
609611^81398-63084768Enzo Doria11/2012
6097(25*2^281577-1)/2384764Lelio R Paula02/2014
60982^281500-45584740Yves Minet03/2012
609910^84725+114514191984726Marisa Kirisame03/2015
610010^84725+14204184726Patrick De Geest10/2015
610110^84725-13867784725Patrick De Geest02/2016
610276^45044+7584720Norbert Schneider02/2015
610354^48897-5384709Norbert Schneider08/2014
6104(9913*2^281377-1)/6584706Lelio R Paula04/2015
6105Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
61062^281337-11122384691Enzo Doria05/2014
61072^281308+5461584683Lelio R Paula09/2013
61087*5^121144-684677Lelio R Paula10/2014
6109(2^281270+3858)/284671Stefano Morozzi01/2020
6110(2^281252+47)/384665Lelio R Paula01/2013
611111^81297-315084663Enzo Doria12/2012
61122^281208-30384653Yves Minet02/2012
6113197^36892-284648Lelio R Paula10/2017
6114(21*2^281187+1)/248384644Lelio R Paula01/2013
611511^81247-8484611Lelio R Paula10/2015
61162067^25516+25516^206784595Norbert Schneider11/2019
611817^68747-6484590Lelio R Paula11/2015
6117(2^281002+3718)/284590Stefano Morozzi01/2020
61195^121018-1559684588Enzo Doria02/2013
61206^108702+784587Lelio R Paula11/2014
612110^84582+10067784583Patrick De Geest05/2016
612210^84582-800184582Robert Price03/2016
61231828^25929+25929^182884580Norbert Schneider12/2019
6124(2^280968+1446)/284580Stefano Morozzi01/2020
61253*5^121004-884579Lelio R Paula10/2014
61265^120996-8484573Lelio R Paula10/2015
6127(2^280896+1522)/284558Stefano Morozzi01/2020
6128(10223*2^280881+1)/6841984553Lelio R Paula06/2014
61292^280852+9768184545Yves Minet08/2004
61302^280848-120384544Lelio R Paula09/2013
61315^120946-2484538Lelio R Paula10/2015
61322^280810-211184533Yves Minet08/2013
613311^81161-516084521Enzo Doria01/2013
61342^280737-9384511Lelio R Paula08/2012
6135(2^280737+494)/284510Stefano Morozzi01/2020
6136(2^280717+1166)/284504Stefano Morozzi01/2020
61372^280698+31584499Lelio R Paula09/2013
61383^177099-34084498Lelio R Paula12/2015
6139(5*10^84469-107)/384470Robert Price01/2017
6140(3^177002+7)/669602227216174484436Lelio R Paula12/2012
6141(2^280500-1017)/82384436Lelio R Paula01/2013
614214^73660-584424Lelio R Paula11/2015
6143(2^280405+746)/284411Stefano Morozzi01/2020
6144(19*10^84409-61)/384410Robert Price04/2017
61452^280388+11784406Lelio R Paula08/2012
61462^280389-56653384406Paul Bourdelais03/2013
6147(2^280340+3322)/284391Stefano Morozzi01/2020
6148(141584^16384+1)/6553784390Syoichiro Yamada06/2008
6150119^40652+11884376Norbert Schneider09/2018
6149(2^280291+2274)/284376Stefano Morozzi01/2020
61512^280240-17384361Lelio R Paula08/2012
6152(184*10^84348-1)/384350Robert Price02/2017
61534*10^84346+9384347Robert Price01/2017
61547*2^280156-584337Lelio R Paula08/2014
61558*7^99782-384327Lelio R Paula10/2014
61562^280116+13384324Lelio R Paula08/2012
61572^280118+5461584324Lelio R Paula09/2013
6158(509203*2^280090-1)/384321Lelio R Paula04/2015
61596^108354+4784316Lelio R Paula12/2015
6160(2^280069+462)/284309Stefano Morozzi01/2020
616110^84305+14196384306Patrick De Geest07/2013
616210^84305-5784305Robert Price05/2011
61639^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
616475843!4-3284295Robert Price11/2019
61653^176648-11280484283Enzo Doria06/2014
61666^108310+11584282Lelio R Paula12/2015
6167(11*2^279968-1)/584280Lelio R Paula02/2014
61686^108288-1664384265Enzo Doria02/2013
61692^279917-5869584264Lelio R Paula08/2013
617065^46477+3684259Lelio R Paula01/2016
6171(2^279883+3230)/284253Stefano Morozzi01/2020
6172(2^279876+1422)/284251Stefano Morozzi01/2020
61732^279866-190784249Yves Minet05/2013
6174(3^176580-5)/2807684246Lelio R Paula12/2012
6175(p(17530)#+4)/284246Robert Price09/2017
6176(2*10^84239+1)/384239Serge Batalov07/2009
617818^67103-4184233Lelio R Paula11/2015
617720^64743-4384233Lelio R Paula01/2016
6179(2^279807+2454)/284230Stefano Morozzi01/2020
6180(2^279754+3574)/284215Stefano Morozzi01/2020
6181143^39070+39070^14384209Serge Batalov05/2014
618211^80857-540084204Enzo Doria01/2013
6183(2^279642+3130)/284181Stefano Morozzi01/2020
6184(13*10^84179+161)/384180Robert Price04/2017
61852^279634-11040584179Enzo Doria05/2014
6186(74*10^84170+313)/984171Robert Price11/2017
61872^279582-101784163Lelio R Paula08/2013
6188(22*10^84159-19)/384160Robert Price02/2017
6189p(17513)#/2+51284156Robert Price05/2017
6190(19*10^84144-43)/384145Robert Price10/2017
6191(9*2^279507-1)/13784139Lelio R Paula02/2014
619211^80792-81084137Enzo Doria11/2012
6193(97*10^84134-1)/384136Serge Batalov12/2014
6194p(17507)#/2+3284125Robert Price12/2016
619521485^8224+8224^2148584116Hans Havermann04/2017
61963^176294-34084114Lelio R Paula12/2015
6197(3^176287+4)/219184107Lelio R Paula12/2012
61982^279388-71984105Yves Minet05/2012
6199(22699*2^279378+1)/22184104Lelio R Paula06/2014
6200(2^279343+578)/284091Stefano Morozzi01/2020
62012^279332-11044784088Enzo Doria05/2014
62022^279320+784084Lelio R Paula06/2012
6203127^39966-284081Lelio R Paula10/2017
6204(2^279299+2490)/284078Stefano Morozzi01/2020
6205(2^279301+1694)/284078Stefano Morozzi01/2020
6206(2^279285+962)/284073Stefano Morozzi01/2020
6207(2^279269+1122)/284069Stefano Morozzi01/2020
6208(11*2^279240-1)/9584059Lelio R Paula02/2014
62092^279218-11134784053Enzo Doria05/2014
621035^54435+284052Lelio R Paula05/2013
6211(2^279176+2998)/284041Stefano Morozzi01/2020
6212(31*2^279191-1)/1251152384040Lelio R Paula02/2014
621320996^10059+10059^2099684038Hans Havermann05/2017
621497*10^84033-384035Robert Price01/2017
6215(2^279153+1326)/284034Stefano Morozzi01/2020
6216(2^279155+3534)/284034Stefano Morozzi01/2020
621721234^9067+9067^2123484033Hans Havermann05/2017
6218(134569^16384+1)/284033Richard Fischer06/2018
62192^279095-10971784016Enzo Doria04/2014
6220(2^279054+1438)/284004Stefano Morozzi01/2020
622114^73282-9983991Lelio R Paula11/2015
622221457^8200+8200^2145783979Hans Havermann06/2017
622389*10^83976-783978Robert Price03/2017
62242^278955+17383974Lelio R Paula06/2012
6225(7*2^278851+1)/3983942Lelio R Paula12/2012
6226(9913*2^278844-1)/4080383940Lelio R Paula04/2015
62275^120076-1484683930Enzo Doria02/2013
6228(85*10^83921-1)/383923Robert Price07/2017
6229(2^278770-3)/2383917Lelio R Paula12/2012
6230(10^83916+449)/983916Serge Batalov12/2014
62322^278715+9983902Lelio R Paula06/2012
6231(132109^16384+1)/283902Richard Fischer05/2018
623340235!2-2^4023583899Robert Price09/2015
62342^278698-17183897Lelio R Paula06/2012
6235(19*10^83894-43)/383895Robert Price10/2017
62366^107802+2583887Lelio R Paula12/2015
62378*10^83880+3983881Robert Price01/2017
6238(58*10^83878+23)/983879Robert Price09/2015
62397^99244-9083871Lelio R Paula10/2015
6240(2^278601+1674)/283867Stefano Morozzi01/2020
62412^278554+425783854Lelio R Paula08/2013
62422^278504-10961983839Enzo Doria04/2014
62432^278499+187043383837Enzo Doria05/2016
6244(2^278487+570)/283833Stefano Morozzi01/2020
6245105^41475+10483829Norbert Schneider11/2016
624615^71276-6883828Lelio R Paula11/2015
62472^278464-21641383827Enzo Doria04/2013
6248(2^278440+1602)/283819Stefano Morozzi01/2020
6249(76*10^83816-211)/983817Robert Price10/2017
6250(2^278429+1950)/283816Stefano Morozzi01/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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